Question

A firm is facing an annual interest of 10% and fixedorder cost of $150. If the firm needs total cash of 300,000 peryear, what is the target cash balance using the BAT model.

Answer 1

The optimal cash balance using the BAT model is $7,746.43.

Step-by-step explanation:

The Baumol-Tobin (BAT) model is used to determine the optimal cash balance that minimizes the sum of the costs of holding cash (i.e., opportunity cost) and the transaction costs (i.e., fixed-order costs).

The formula for the optimal cash balance using the BAT model is:

TC = (2DS/i)^0.5 * i/2 + C

Where:

TC = total annual cost of holding cash and making transactions

D = total cash needed per year

S = fixed order cost per transaction

i = annual interest rate (opportunity cost of holding cash)

C = cost of holding one unit of cash for one year (typically half of i)

In this case:

D = $300,000 per year

S = $150 per order

i = 10% (or 0.1)

C = i/2 = 0.05

Plugging these values into the formula, we get:

TC = (2 x $300,000 x $150/0.1)^0.5 x 0.1/2 + 0.05 = $17,320.51

To find the optimal cash balance, we need to find the point where the total cost is minimized. This occurs at the point where the order quantity (Q) equals:

Q = (2DS/i)^0.5

Plugging in the values we get:

Q = (2 x $300,000 x $150/0.1)^0.5 = $7,746.43

Therefore, the optimal cash balance using the BAT model is $7,746.43.